Negative voltage in Arduino

You might also look at CMOS opAmps labelled as "rail-to-rail" input and
output. They should run off single-sided 0-5V power.

+5 ---| R1 |--- + ---| R2 | --- GND
                |
                | <- audio GND

This "audio ground" connects to the ground of the incoming audio 
signal.  Do NOT connect this to your Arduino circuit GND, otherwise 
you'll have a short.

I don't understand what is being said here at all. ????

I think the proper thing to do is to use a voltage-divider on the analog signal,
in order to raise the reference level up so the negative part of the AC isn't
clipped.

However, where it says "Audio GND", that should read "audio signal", on
the one side and there should be another wire going "up" to an Arduino
A/D channel. And simply connect the Arduino and audio grounds together.
Plus, you should also insert a capacitor, say 1-uF to 10-uF, to block the
2.5VDC from getting back to the audio side.

Also, if your audio signal has larger swing than +/-2.5V, you can insert
another R in series with the capacitor, so the total voltage divider effect
will become 5K / (R + 5K), where the 5K comes from 10K parallel 10K.
Eg, if R=5K, then you can apply a +/-5VAC signal.

              A/D channel
                |
+5 --| 10K |--- + --| 10K | --- GND
                |
               --- +
               10uF
               ---
                |
                R (5K)
                |
                | <- audio signal